Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration A. - - PowerPoint PPT Presentation

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Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration A. - - PowerPoint PPT Presentation

Apr 13, 2023 408 likes •731 views

Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration A. B. Kahng, 180327 ISPD--2018 Influence of Professor T. C. Hus Works on Fundamental Approaches in Layout Andrew B. Kahng CSE and ECE Departments UC San Diego

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  • A. B. Kahng, 180327 ISPD--2018

Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration

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  • A. B. Kahng, 180327 ISPD--2018

Influence of Professor T. C. Hu’s Works on Fundamental Approaches in Layout

Andrew B. Kahng CSE and ECE Departments UC San Diego http://vlsicad.ucsd.edu

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  • A. B. Kahng, 180327 ISPD--2018

Professor T. C. Hu

  • Introduced combinatorial optimization, and

mathematical programming formulations and methods, to VLSI Layout

  • Many works reflect unique ability to combine

geometric, graph-theoretic, and combinatorial- algorithmic ideas

  • 1961: Gomory-Hu cut tree
  • 1973: Adolphson-Hu cut-based linear placement
  • 1985: Hu-Moerder hyperedge net model
  • 1985: Hu-Shing - routing
  • Applications of duality: flows and cuts, shadow

price  Professor C.-K. Cheng in next talk

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  • A. B. Kahng, 180327 ISPD--2018

Professor T. C. Hu

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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

TACP and Shadow Price (1)

  • TACP: tentative assignment and competitive pricing
  • Application: Fixed-outline floorplanning
  • Fixed die, fixed block aspect ratio

 classical “packing” that minimizes whitespace, etc. !!!

  • Seeks “perfect” rectilinear floorplanning: zero whitespace
  • Irregular block shape
  • Overlapping blocks
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  • A. B. Kahng, 180327 ISPD--2018

TACP and Shadow Price (2)

  • Shadow price in linear programming duality
  • Primal-dual iterations in global routing
  • Local density in global placement
  • Global density
  • More recent: constraint-oriented local density

m ⋅ m Σ ⋅

Better cell spreading, better wirelength!

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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

Linear Placement

  • Optimal linear ordering (O.L.O.) problem
  • pins in holes, 1 pin per hole
  • Holes in a line, unit distance apart
  • Minimize the wirelength
  • Gomory and Hu / Adolphson and Hu
  • 1/2 max flow values between any source / sink

nodes can be obtained with 1 max flow problems, giving 1 fundamental cuts

  • 1 fundamental cuts are lower bound for O.L.O.

The min-cut defines an ordered partition that is consistent with an optimal vertex

  • rder in the linear placement problem.
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  • A. B. Kahng, 180327 ISPD--2018

Minimum Cuts in Placement

  • Recursive min-cut
  • [Cheng87]: universal application to VLSI placement
  • Capo: top-down, min-cut bisection
  • Feng Shui: general purpose mixed-size placer
  • Duality between max flows and min cuts
  • [Yang96]: flow-based balanced netlist bipartition
  • MLPart: multilevel KL-FM/ flat KL-FM / flow-based partitioning
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  • A. B. Kahng, 180327 ISPD--2018

Linear Placements Today

  • Single-row placement
  • Variable cell width
  • Fixed row length with free sites
  • Fixed cell ordering
  • Multi-row placement
  • Local layout effect-aware
  • Reorderable cells
  • Support of multi-height cells
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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

Net Modeling

  • “Multiterminal Flows in a Hypergraph”, Hu and

Moerder, 1985

  • Challenging question:
  • How should a hyperedge of a hypergraph be modeled by

graph edges in a graph model of the hypergraph?

  • Applications for analytic placement, for exploiting sparse-

matrix codes for layouts

  • New hyperedge net model - p pin nodes and one

star node to represent a p-pin hyperedge

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  • A. B. Kahng, 180327 ISPD--2018
  • Transform netlist hypergraph
  • Add one star node for each signal net
  • Connect star node to each pin node (via a graph edge)
  • Sparse, symmetric + exactly captures true cut cost
  • Star model: [Brenner01], BonnPlace [Brenner08]

Example Transformation

Example circuit with 5 modules and 3 nets Equivalent hypergraph model

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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

The Prim-Dijkstra Tradeoff

  • Prim’s Minimum Spanning Tree (MST)
  • Iteratively add edge eij to T, such that vi ϵ T, vi ∉ T and dij is minimum
  • Minimizes tree wirelength (WL)
  • Dijkstra’s Shortest Path Tree (SPT)
  • Iteratively add edge eij to T, such that vi ϵ T, vi ∉ T and li + dij is

minimum (where l is source-to-sink pathlength of v)

  • Minimizes source-to-sink pathlengths (PLs)
  • Prim-Dijkstra Tradeoff (Alpert, Hu, Huang, Kahng, 1993)
  • “PD1” tradeoff: iteratively add eij to T that minimizes c  li + dij
  • c = 0  Prim’s MST
  • c = 1  Dijkstra’s SPT // c enables balancing of tree WL, source-sink PLs
  • “PD2” tradeoff: iteratively add eij to T that minimizes ( li

p + dij )1/p

  • p = ∞  Prim’s MST;
  • p = 1  Dijkstra’s SPT
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  • A. B. Kahng, 180327 ISPD--2018

Prim-Dijkstra Construction

Prim’s Minimum Spanning Tree (MST) Minimizes wirelength

Dijkstra’s Shortest Path Tree (SPT) Minimizes source-sink pathlengths Prim-Dijkstra (PD) tradeoff Directly trades off the Prim, Dijkstra constructions

But large pathlengths to nodes 3,4,5

2 1 3 4 5 2 1 3 4 5

But large tree wirelength!

2 1 3 4 5

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  • A. B. Kahng, 180327 ISPD--2018

PD Tradeoff: 25 Years of Impact

  • Widely used
  • In EDA for timing estimation, buffer tree construction and

global routing

  • In flood control, biomedical, military, wireless sensor

networks, etc.

  • Simple and fast – O(n log n)
  • Alpert et al., DAC06: PD is practically ‘free’
  • Yesterday: “PD Revisited”
  • Iterative repair of spanning tree
  • Detour-aware Steinerization
  • Better WL, PL tradeoff
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  • A. B. Kahng, 180327 ISPD--2018

A Few Examples

  • Tentative Assignment / Competitive Pricing
  • Optimal Linear Ordering
  • Hyperedge Net Model
  • The Prim-Dijkstra Tradeoff
  • The Discrete Plateau Problem and Finding a Wide

Path

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  • A. B. Kahng, 180327 ISPD--2018

Connection Finding

  • Basic element of any routing approach
  • routing (Hu and Shing, 1985)
  • Find connections given edge and vertex costs
  • Comprehend existence of “turn” at vertex
  • Provide unified elements for
  • Dijkstra’s algorithm
  • Best-first (A*) search
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  • A. B. Kahng, 180327 ISPD--2018
  • Proc. Nat. Acad. Sci., October 1992
  • Discrete version of

Plateau’s minimum- surface problem

  • Solved using duality of

cuts and flow

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  • A. B. Kahng, 180327 ISPD--2018

Towards Robust (Wide) Path Finding

  • Robust path finding problem
  • Source-destination routing with prescribed width
  • Seek minimum-cost path that has robustness (width) = d
  • E.g., a mobile agent with finite width
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  • A. B. Kahng, 180327 ISPD--2018

Network Flow Approach

  • Discretize routing environment
  • A minimum cut in flow network
  • Contain all vertices and edges on a robust path
  • Correspond to a maximum flow by duality
  • Return a robust path
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  • A. B. Kahng, 180327 ISPD--2018

Applications Today

  • Relevant to many difficult problems
  • Bus routing, bus feedthrough determination, etc.
  • IC package routing
  • Per-net PI/SI requirement
  • Need traces of various width
  • Wide path finding (with multiple commodities) can be useful
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  • A. B. Kahng, 180327 ISPD--2018

Conclusion

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  • A. B. Kahng, 180327 ISPD--2018
  • T. C. Hu
  • W. T. Torres

K-C. Tan

  • Y. S. Kuo
  • P. A. Tucker
  • A. B. Kahng
  • K. E. Moerder

M.-T. Shing

  • F. Ruskey
  • D. Adolphson
  • B. N. Tien

D.R. van Baronaigien

  • Y. Koda
  • P. Evans
  • A. Smith
  • K. Wong
  • J. Sawada
  • S. Chow

M.R. Kindl M.M. Cordeiro

  • J. Chen
  • G. Robins

C.J. Alpert K.D. Boese

  • Y. Chen
  • K. Masuko
  • P. Gupta
  • L. Hagen

D.J. Huang

  • B. Liu
  • S. Mantik
  • I. Markov
  • S. Muddu
  • S. Reda

C-W.A. Tsao

  • Q. Wang
  • X. Xu
  • M. Alexander
  • T. Zhang

A Ramani

  • S. Adya
  • G. Pruesse
  • G. Thomas
  • A. Zaki

S-J. Su Y-H. Hsu C-C. Jung

Professor Hu’s 96 Ph.D. Descendants

  • S. Kang
  • C. H. Park
  • W. Chan
  • S. Muddu
  • K. Samadi
  • K. Jeong
  • R. O. Topaloglu
  • T. Chan
  • P. Sharma
  • S. Nath
  • J. Li
  • M. Weston
  • B. Bultena
  • A. Erickson
  • A. Mamakani
  • V. Irvine
  • A. Williams
  • L. Bolotnyy
  • C. Taylor
  • K. Chawla
  • R. Layer
  • N. Brunelle
  • A. M. Eren
  • G. Xu
  • V. Maffei
  • G. Viamontes

K-H. Chang

  • S. Krishnaswamy
  • S. Plaza
  • J. Roy
  • D. Papa
  • D. Lee
  • M. Kim
  • J. Hu
  • H. J. Garcia
  • R. Cochran
  • N. Abdullah
  • K. Nepal
  • K. Dev
  • X. Zhan
  • S. Hashemi
  • R. Azimi
  • J. Lee
  • L. Cheng
  • R. Ghaida
  • A. A. Kagalwalla
  • L. Lai
  • M. Gottscho
  • S. Wang
  • Y. Badr
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  • A. B. Kahng, 180327 ISPD--2018

Thank you, Professor Hu.

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  • A. B. Kahng, 180327 ISPD--2018
  • Hypergraph net model
  • Sparse and symmetric
  • Enables exact representation of net cut cost
  • Challenges
  • Large memory footprint for rewriting netlist - need

sophisticated memory pool management and containers

  • Current systems make this feasible!
  • Star net-model - separately realized in other works
  • E.g.: Defined in [Brenner01] and used in BonnPlace

[Brenner08]

Hypergraph Model - Useful Qualities

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  • A. B. Kahng, 180327 ISPD--2018
  • Show: Max-flow min-cut theorem can find a

minimum-cut bipartitioning of a hypergraph

  • Algorithm
  • Construct a tree - flow-equivalent to a given hypergraph
  • Similar to the Gomory-Hu cut-tree

Minimum-cut Bipartitioning